Representations of the Lie algebra of vector fields on a sphere
For an affine algebraic variety X we study a category of modules that admit compatible actions of both the algebra A of functions on X and the Lie algebra of vector fields on X. In particular, for the case when X is the sphere S2, we construct a set of simple modules that are finitely generated over A. In addition, we prove that the monoidal category that these modules generate is equivalent to the category of finite-dimensional rational GL2-modules.
|Journal of Pure and Applied Algebra|
|Organisation||School of Mathematics and Statistics|
Billig, Y, & Nilsson, J. (Jonathan). (2018). Representations of the Lie algebra of vector fields on a sphere. Journal of Pure and Applied Algebra. doi:10.1016/j.jpaa.2018.11.018